A finite element model for the analysis of inflation of a thick polymer sheet has been developed. The major objective was the creation of an algorithm for polymer thermoforming without the use of the thin membrane approximation. The model incorporates axisymmetric geometry, total Lagrangian description, and isothermally hyperelastic behavior (Mooney model) with incompressibility. It has the capabilities to deal with the free inflation of single layer or multilayer polymeric sheets of finite thickness. Comparison with experimental data available in the literature for single layer sheets of rubber (Treloar, 1944) and PMMA (Lai and Holt, 1975) indicates very good agreement.